Early T-cell activation is selected by evolution to discriminate a few foreign peptides rapidly from a vast excess of self-peptides, and it is unclear in quantitative terms how this is possible. It will be discussed how a generic proofreading cascade supplemented by a single negative feedback accounts quantitatively for early T-cell activation, including antagonistic effects. Modulation of the negative feedback mediated by the SHP-1 phosphatase explains previous counterintuitive observations and new experiments validate predictions. Absolute limits on the tradeoffs between decision speed and accuracy are then explored. In addition to the immune system, rapidly developing embryos, and cellular response to stress, provide examples where fast and accurate actions are required. Statistical theory under the rubric of 'exploit-explore' supplies rigorous performance bounds and algorithms that realize them. It will be shown that common protein phosphorylation networks can implement optimal decision theory algorithms, and speculated that the ubiquitous chemical modifications to receptors during signaling actually perform such analogue computations.